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prisoha [69]
3 years ago
8

I need help with this urgently!!

Mathematics
1 answer:
galben [10]3 years ago
3 0

Answer:

c

Step-by-step explanation:

your welcome

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Integral of 17/(x^3-125)
daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0
3 years ago
Evaluate –3² + (2 – 6)(10)<br> i got -72 some how oof
djverab [1.8K]

Answer: -49

Step-by-step explanation:  hope this helps you and plz mark me as brainest

7 0
2 years ago
Read 2 more answers
Pls answer math<br> need help quick!!<br> look at the attached file below for question
harkovskaia [24]
Remark
I didn't know this was a calculus question. How dumb of me.

f(x + h) - f(x)
==========
x + h  - h

50/6 - 51/6 =( -1/6+ h)/h 
The h's will disappear when the limit is taken.

answer - 1/6 which is A. If anyone else answers take their answer. 


7 0
3 years ago
A salesman gets a commission of 2.4% on sales up to sh. 100,000. He gets an additional commission of 1.5% on sales above this. C
emmainna [20.7K]

Answer:

Sh. 10,920

Step-by-step explanation:

Since the sales is above sh. 100,000,his commission is (2.4+1.5) 3.9%.

3.9% of 280,000= 10920.

Therefore, his commission is sh. 10,920

6 0
3 years ago
What is the slope of the line passing through the points (2,7) and (-1,3)?
e-lub [12.9K]
The slope of the line is 4/3
5 0
3 years ago
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